The theatre, complete with dress circle and teaching gallery, is part of a £22.5m capital development project which began construction in the summer of 2009 and is due for completion in the spring of 2011.
It will also include a 450-capacity "world-class" concert hall, an exhibition arcade and four new acting and movement studio.
The RWCMD will also have a new entrance leading on to a central foyer and performance spaces, as well as a new café bar and terrace overlooking Bute Park.
Burton's nephew Guy Masterson said the Burton family was "deeply appreciative of the naming of this wonderful theatre".
"Wales has given the world some of its greatest artistes, and we are delighted that Rich's legacy lives on in his homeland," said Mr Masterson.
"We are confident that it will provide a great environment for the students at the Royal Welsh College."
Kate Burton, Richard Burton's daughter, who was unable to be at gala due to work commitments in the US, added: 'I am proud and very excited about the naming of this theatre for my father.
"He was a very passionate and determined man and I know this new theatre in the capital of Wales will inspire future generations of young actors to follow in his footsteps.'
He was a very passionate and determined man and I know this new theatre in the capital of Wales will inspire future generations of young actors to follow in his footsteps
Kate Burton, daughter
College principal Hilary Boulding, added: "Richard Burton is synonymous with a passion and talent for acting, and commemorating his legacy in this way will be an inspiration for our students. We are delighted that Wales' newest theatre will bear his name."
The Prince of Wales, patron of the college, hosted the royal gala at Buckingham Palace as the culmination of the college's 60th anniversary celebrations.
At the gala Dame Elizabeth presented the Prince with an original bronze bust of the actor as a young man, which will stand in the foyer of the new Richard Burton Theatre.
"It is wonderful to be here and join in this celebration, along with many others who remember and respect Richard with so much love in their hearts," Dame Elizabeth added.
Burton was born Richard Walter Jenkins in Pontrhydyfen on 10 November 1925, the 12th of 13 children. The Jenkins family was working class and Welsh speaking, and his father worked in the mines.
He had a talent for English and Welsh literature at school and was later adopted by his influential schoolmaster Philip Burton.
After serving in the Second World War as an RAF navigator he moved to London to find work as an actor.
His profile rose as he gave one acclaimed stage performance after another and after moving to Hollywood he established himself as a major force while continuing his well received theatre work.
In 1963 Burton starred as Mark Antony in the epic movie Cleopatra opposite Taylor in the title role and on set the two actors, both married to other people, fell in love.
It marked the start of a tempestuous relationship and a succession of film roles together followed including The Sandpiper (1965), Who's Afraid Of Virginia Woolf? (1966) and The Taming Of The Shrew (1967).
The couple divorced in 1974 before re-marrying the following year but the second union lasted less than 12 months. Burton died in 1984.
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